If $f(x)=2^x$, then show that $f(x)\cdot f(y)=f(x+y)$.

If f(x)=2x, then show that f(x)· f(y)=f(x+y).

Question 40 of 49

f(x)=2^x

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2024Subjective· 2mImportance★★★★★

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Since $2^x\cdot2^y=2^{x+y}$ , the function $f(x)=2^x$ satisfies $f(x)f(y)=f(x+y)$ .

Given $f(x)=2^{x}$ .

LHS: $\ f(x)\cdot f(y)=2^{x}\cdot 2^{y}.$

Law of exponents $a^{m}a^{n}=a^{m+n}$ : $\ 2^{x}\cdot2^{y}=2^{x+y}.$

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